The method for probing by wave propagation uses an assembly of transducers and allows for example measuring a characteristic parameter of the medium, and/or detecting a singular point of the medium, and/or creating an image of the medium.
Methods of this type are used in particular in detection and imaging systems, for example such as sonar, radar, ultrasound, etc.
In known methods of this type and in particular in ultrasound or radar imaging methods, a simple-scattering component of the captured signals is used: if each scatterer only interacts once with the wave, there is effectively a direct equivalence between the time of arrival of each echo and the distance separating the transducer and the scatterer that generated this echo. Detection of an echo at a given moment is indicative of the presence of a scatterer at the distance corresponding to the time of arrival of the echo. An image of the reflectivity of the medium, meaning the position of the various scatterers within the medium, can then be constructed from the received signals if necessary. Multiple scattering is not much used in ultrasound or radar imaging methods. These imaging methods are based on the assumption that there is negligible multiple scattering.
In the presence of a significant multiple-scattering component, particularly when scatterers contained in the medium have a high scattering power and/or are very dense within the medium, conventional imaging methods are greatly disrupted and are no longer reliable. Indeed, in this case, there is no equivalence between the time of arrival of an echo and the distance separating a transducer and a scatterer of the medium, which does not enable constructing an image of the medium.
Patent application WO-2010/001027 proposes a probing method capable of separating the multiple-scattering component from the simple-scattering component. More particularly, the method of that document comprises the following steps:
(a) an emitting step during which an assembly of transducers (meaning some or all of the transducers of the assembly) emits an incident wave in a medium which scatters said wave,
(b) a measuring step during which said assembly of transducers (meaning some or all of the transducers of the assembly) captures signals representative of a reflected wave reverberated by the medium from the incident wave, said captured signals comprising:                a simple-scattering component, representative of wave paths where the reflected wave results from a single reflection of the incident wave by each scatterer of the medium,        and where appropriate a multiple-scattering component, representative of wave paths where the reflected wave results from multiple successive reflections of the incident wave on the scatterers of the medium before reaching the assembly of transducers,        
(c) a processing step during which said captured signals are processed in order to determine characteristics of the medium (the characteristics in question may consist of an image of the medium, and/or a value of a parameter of the medium, and/or the presence or absence of a singular point such as heterogeneity, etc.), at least one component selected among the multiple-scattering component and the simple-scattering component is extracted by filtering at least one frequency transfer matrix representative of responses between transducers of the assembly of transducers, and which comprises at least the following substeps:
(c1) a windowed transfer matrix determination substep during which is determined at least one windowed frequency transfer matrix K(T,f) corresponding to a windowed temporal matrix of inter-element response K(T,t)=[kij(T,t)] (or response between transducers of the assembly), said windowed temporal matrix of inter-element response corresponding, over a time window close to a time T and of duration Δt, to the temporal responses hij(t) between transducers of the assembly of transducers, f being the frequency,
(c2) a data rotation substep during which two matrices A1(T,f) and A2(t,f) are calculated from the windowed frequency transfer matrix K(T,f), by rotations in a first direction and extraction of components from the windowed frequency transfer matrix,
(c3) a filtering substep during which the multiple-scattering component is separated from the simple-scattering component in each of matrices A1, A2, thus obtaining at least two filtered matrices A1F, A2F respectively corresponding to matrices A1, A2 and each representative of either the simple-scattering component or the multiple-scattering component,
(c4) a reverse data rotation substep during which a filtered windowed transfer matrix KF(T,f) is calculated from the two filtered matrices A1F, A2F by rotations in a second direction opposite the first direction and extraction of components from the filtered matrices A1F, A2F.